Ubuntu boots to "Read Only Filesystem" after Upgrading

Start the computer with a live-dvd/usb.

After the load open a terminal,

Press Ctrl+Alt+T

Run it:

$ sudo -i
# fdisk -l

Fdisk will inform your partitions as they are called, something like:

Disk /dev/sda: 74,5 GiB, 80032038912 bytes, 156312576 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: dos
Disk identifier: 0xab6eab6e

Device     Boot    Start       End   Sectors  Size Id Type
/dev/sda1  *        2048  54750094  54748047 26,1G 83 Linux
/dev/sda2       54751230 156311551 101560322 48,4G  5 Extended
/dev/sda5       54751232  56702975   1951744  953M 82 Linux swap / Solaris
/dev/sda6       56705024 156311551  99606528 47,5G 83 Linux

For each of the Linux partitions, run the following commands:

# umount /dev/sda?    
# fsck -y /dev/sda?

In the example would:

# umount /dev/sda1    
# umount /dev/sda6    
# fsck -y /dev/sda1
# fsck -y /dev/sda6

Then continue running, assuming that / is /dev/sda1:

# mount /dev/sda1 /mnt
# mount --bind /dev /mnt/dev 
# mount --bind /dev/pts /mnt/dev/pts
# mount --bind /proc /mnt/proc
# mount --bind /sys /mnt/sys
# mount --bind /etc/resolv.conf /mnt/etc/resolv.conf
# chroot /mnt
# dpkg --configure -a
# apt-get -f install
# apt-get update
# apt-get dist-upgrade
# apt-get autoremove
# apt-get clean
# umount /mnt
# exit
# reboot